Question

An arc with length 5 pi over 4 inches is formed by a 15 degree central angle what is the radius of the circle

Answer 1

Radius of the circle is 15 inches.

Explanation:

Relation between length of arc, radius and the angle subtended by the arc on center is:

`\theta = (l)/(r) ..... (1)`

where
`\theta` is the central angle in radians subtended by arc

`l` is the length of arc

`r` is the radius of arc

We are Given the following details:

`l = (5\pi)/(4)\ inch`

`\theta = 15^\circ`

We know that
`\pi \ radians = 180 ^\circ`

Converting
`\theta` to radians:

`\theta =(\pi)/(180) * 15` radians

Putting the values of
`\theta` and
`l` to find the value of
`r`

`(\pi)/(180) * 15 = (5\pi)/(4r)\\\Rightarrow r = (45)/(3) \\\Rightarrow r = 15 \ inches`

Hence, Radius of the circle is 15 inches.